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Question
Find the area of a right-angled triangle whose hypotenuse is 13 cm long and one of its legs is 12 cm long.
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Solution
In right-angled Δ ABC,
Base BC = 12 cm
and hypotenuse AC = 13 cm
Applying Pythagoras Theorem,
(AC)2 = (AB)2 + (BC)2
(13)2 = (AB)2 + (12)2
169 = (AB)2 + 144
(AB)2 = 169 − 144
(AB)2 = 25
∴ AB =`sqrt25`
= `sqrt(5xx5)` = 5 cm
Now, area of Δ ABC =`1/2"base"xx"altitude"`
= `1/2xx12xx5` = 30 cm2
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